Apparaît dans la collection : Combinatorial geometries: matroids, oriented matroids and applications / Géométries combinatoires : matroïdes, matroïdes orientés et applications
A cube is a matroid over $C^n={-1,+1}^n$ that contains as circuits the usual rectangles of the real affine cube packed in such a way that the usual facets and skew-facets are hyperplanes of the matroid. How many cubes are orientable? So far, only one: the oriented real affine cube. We review the results obtained so far concerning this question. They follow two directions: 1)Identification of general obstructions to orientability in this class. (da Silva, EJC 30 (8), 2009, 1825-1832). 2)(work in collaboration with E. Gioan) Identification of algebraic and geometric properties of recursive families of non-negative integer vectors defining hyperplanes of the real affine cube and the analysis of this question and of las Vergnas cube conjecture in small dimensions.
De Viviane Pons
De Viviane Pons
De Stephen Coombes , Peter Liddle
De Victor Kleptsyn
De Albert Schwarz
